What is the 90-degree angle theory?

Understanding the 90-Degree Angle Theory

In geometry, a right triangle is a polygon with one 90-degree angle, also known as a right angle. The sides adjacent to the right angle are called the legs, while the side opposite the right angle is called the hypotenuse. The relationship between the sides of a right triangle is governed by the Pythagorean theorem.

Pythagorean Theorem and the 90-Degree Angle

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b). Mathematically, it can be expressed as:

c² = a² + b²

This theorem holds true only for right triangles, and it provides a crucial test for determining if a given triangle is a right triangle.

Definition of a 90-Degree Angle Using the Pythagorean Theorem

Using the Pythagorean theorem, we can precisely define a 90-degree angle between two sides of a triangle:

If the square of the length of one side (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), then the angle between sides a and b is a 90-degree angle.

In other words, if the Pythagorean theorem is satisfied for three sides, then the triangle is a right triangle, and the angle between the two shorter sides is a right angle.

Applications of the 90-Degree Angle Theory

The 90-degree angle theory has numerous applications in various fields, such as:

• Architecture: Determining the height of a building or the distance between two points using trigonometry.
• Construction: Ensuring the accuracy of right-angled joints in structures.
• Engineering: Calculating forces and stresses in structures and machines.
• Navigation: Determining the distance and direction between points using right-angled triangles.
• Surveying: Measuring distances and angles in land surveys.

By understanding the 90-degree angle theory and the Pythagorean theorem, individuals can gain insights into the relationships between sides of right triangles and apply these principles to solve practical problems and make accurate measurements.